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Identification of LTI Time-Delay Systems with Missing Output Data Using GEM Algorithm

MATHEMATICAL PROBLEMS IN ENGINEERING 2014年第1期2014卷 1-8页

作者： Yang, Xianqiang Karimi, Hamid Reza Harbin Inst Technol Res Inst Intelligent Control & Syst Harbin 150080 Heilongjiang Peoples R China Univ Agder Dept Engn Fac Sci & Engn N-4898 Grimstad Norway

This paper considers the parameter estimation for linear time-invariant (LTI) systems in an input-output setting with output error (OE) time-delay model structure. The problem of missing data is commonly experienced in industry due to irregular sampling, sensor failure, data deletion in data preprocessing, network transmission fault, and so forth;to deal with the identification of LTI systems with time-delay in incomplete-data problem, the generalized expectation-maximization (GEM) algorithm is adopted to estimate the model parameters and the time-delay simultaneously. Numerical examples are provided to demonstrate the effectiveness of the proposed method.

关键词： LINEAR time invariant systems TIME delay systems MISSING data (Statistics) expectation-maximization algorithms GENERALIZABILITY theory (Statistics)

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Simultaneous curve registration and clustering for functional data

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2009年第4期53卷 1361-1376页

作者： Liu, Xueli Yang, Mark C. K. Univ Florida Dept Stat Gainesville FL 32611 USA

Study of dynamic processes in many areas of science has led to the appearance of functional data sets. It is often the case that individual trajectories vary both in the amplitude space and in the time space. We develop a coherent clustering procedure that allows for temporal aligning. Under this framework, closed form solutions of an EM type learning algorithm are derived. The method can be applied to all types of curve data but is particularly useful when phase variation is present. We demonstrate the method by both simulation studies and an application to human growth curves. Published by Elsevier B.V.

关键词： DATA analysis CLUSTER analysis (Statistics) DATA structures (Computer science) expectation-maximization algorithms STOCHASTIC approximation ANALYSIS of variance

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Dynamic Compressive Sensing of Time-Varying Signals Via Approximate Message Passing

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2013年第21期61卷 5270-5284页

作者： Ziniel, Justin Schniter, Philip Ohio State Univ Dept Elect & Comp Engn Columbus OH 43210 USA

In this work the dynamic compressive sensing (CS) problem of recovering sparse, correlated, time-varying signals from sub-Nyquist, non-adaptive, linear measurements is explored from a Bayesian perspective. While there has been a handful of previously proposed Bayesian dynamic CS algorithms in the literature, the ability to perform inference on high-dimensional problems in a computationally efficient manner remains elusive. In response, we propose a probabilistic dynamic CS signal model that captures both amplitude and support correlation structure, and describe an approximate message passing algorithm that performs soft signal estimation and support detection with a computational complexity that is linear in all problem dimensions. The algorithm, DCS-AMP, can perform either causal filtering or non-causal smoothing, and is capable of learning model parameters adaptively from the data through an expectation-maximization learning procedure. We provide numerical evidence that DCS-AMP performs within 3 dB of oracle bounds on synthetic data under a variety of operating conditions. We further describe the result of applying DCS-AMP to two real dynamic CS datasets, as well as a frequency estimation task, to bolster our claim that DCS-AMP is capable of offering state-of-the-art performance and speed on real-world high-dimensional problems.

关键词： Approximate message passing (AMP) belief propagation compressed sensing expectation-maximization algorithms time-varying sparse signals Kalman filters dynamic compressive sensing statistical signal processing

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ESTIMATION algorithms FOR DYNAMIC TRACER STUDIES USING POSITRON-EMISSION TOMOGRAPHY

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IEEE TRANSACTIONS ON MEDICAL IMAGING 1987年第2期6卷 115-125页

作者： OLLINGER, JM WASHINGTON UNIV INST BIOMED COMP ST LOUIS MO 63130 USA WASHINGTON UNIV DEPT ELECT ENGN ST LOUIS MO 63130 USA

algorithms are developed for estimating statistics for use by parameter estimation algorithms in dynamic tracer studies utilizing positron-emission tomography and requiring high temporal resolution. Two types of statistics are considered. One can be used with the expectation-maximization algorithm to compute maximum likelihood parameter estimates, and the other computes a histogram of activity levels versus time for use with weighted least squares parameter estimation algorithms. An estimator of the variance of this histogram is also given. Variants for use with both time-of-flight and projection data collected at high frame rates are presented. The algorithms account for the effects of attenuation, randoms, detector efficiency, and nonuniform sampling.

关键词： Heuristic algorithms Tomography Parameter estimation Statistics Histograms expectation-maximization algorithms Maximum likelihood detection Maximum likelihood estimation Least squares approximation Attenuation

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Theoretical Foundation for CMA-ES from Information Geometry Perspective

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ALGORITHMICA 2012年第4期64卷 698-716页

作者： Akimoto, Youhei Nagata, Yuichi Ono, Isao Kobayashi, Shigenobu Univ Paris 11 TAO Team INRIA Saclay LRI F-91405 Orsay France Tokyo Inst Technol Interdisciplinary Grad Sch Sci & Engn Yokohama Kanagawa 2268502 Japan

This paper explores the theoretical basis of the covariance matrix adaptation evolution strategy (CMA-ES) from the information geometry viewpoint. To establish a theoretical foundation for the CMA-ES, we focus on a geometric structure of a Riemannian manifold of probability distributions equipped with the Fisher metric. We define a function on the manifold which is the expectation of fitness over the sampling distribution, and regard the goal of update of the parameters of sampling distribution in the CMA-ES as maximization of the expected fitness. We investigate the steepest ascent learning for the expected fitness maximization, where the steepest ascent direction is given by the natural gradient, which is the product of the inverse of the Fisher information matrix and the conventional gradient of the function. Our first result is that we can obtain under some types of parameterization of multivariate normal distribution the natural gradient of the expected fitness without the need for inversion of the Fisher information matrix. We find that the update of the distribution parameters in the CMA-ES is the same as natural gradient learning for expected fitness maximization. Our second result is that we derive the range of learning rates such that a step in the direction of the exact natural gradient improves the parameters in the expected fitness. We see from the close relation between the CMA-ES and natural gradient learning that the default setting of learning rates in the CMA-ES seems suitable in terms of monotone improvement in expected fitness. Then, we discuss the relation to the expectation-maximization framework and provide an information geometric interpretation of the CMA-ES.

关键词： CMA-ES Information geometry Natural gradient learning expectation-maximization algorithms Expected fitness maximization Continuous optimization

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Hidden Markov Models for the Stimulus-Response Relationships of Multistate Neural Systems

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NEURAL COMPUTATION 2011年第5期23卷 1071-1132页

作者： Escola, Sean Fontanini, Alfredo Katz, Don Paninski, Liam Columbia Univ Ctr Theoret Neurosci New York NY 10032 USA SUNY Stony Brook Dept Neurobiol & Behav Stony Brook NY 11794 USA Brandeis Univ Dept Psychol Waltham MA 02453 USA Columbia Univ Dept Stat New York NY 10032 USA

Given recent experimental results suggesting that neural circuits may evolve through multiple firing states, we develop a framework for estimating state-dependent neural response properties from spike train data. We modify the traditional hidden Markov model (HMM) framework to incorporate stimulus-driven, non-Poisson point-process observations. For maximal flexibility, we allow external, time-varying stimuli and the neurons' own spike histories to drive both the spiking behavior in each state and the transitioning behavior between states. We employ an appropriately modified expectation-maximization algorithm to estimate the model parameters. The expectation step is solved by the standard forward-backward algorithm for HMMs. The maximization step reduces to a set of separable concave optimization problems if the model is restricted slightly. We first test our algorithm on simulated data and are able to fully recover the parameters used to generate the data and accurately recapitulate the sequence of hidden states. We then apply our algorithm to a recently published data set in which the observed neuronal ensembles displayed multistate behavior and show that inclusion of spike history information significantly improves the fit of the model. Additionally, we show that a simple reformulation of the state space of the underlying Markov chain allows us to implement a hybrid half-multistate, half-histogram model that may be more appropriate for capturing the complexity of certain data sets than either a simple HMM or a simple peristimulus time histogram model alone.

关键词： HIDDEN Markov models NEURAL stimulation NEURAL networks (Computer science) NEURAL circuitry POISSON processes expectation-maximization algorithms SIMULATION methods & models

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From yield history to productivity zone identification with hidden Markov random fields

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PRECISION AGRICULTURE 2020年第4期21卷 762-781页

作者： Layton, Alex Krogmeier, James V. Ault, Aaron Buckmaster, Dennis R. Purdue Univ Sch Elect & Comp Engn 465 Northwestern Ave W Lafayette IN 47907 USA Purdue Univ Sch Agr & Biol Engn 225 S Univ St W Lafayette IN 47907 USA

Modern precision agriculture equipment enables site-specific management by allowing different treatments for different parts of a field. This ability to subdivide the field calls for identifying management zones. A compromise between treating a field uniformly and treating every plant individually is needed, as the former does not maximize yields and the latter is often impractical. This work presents an algorithm for inferring the yield productivity zones (YPZ) for a field based on yield data from multiple years. The algorithm uses a hidden Markov random field model (HMRF) to find regions of the field which likely correspond to the same underlying yield distribution (i.e., productivity zones). These regions are modeled to be the same every year, but their distributions (i.e., yield characteristics) are allowed to vary with time to account for year-to-year variability (from e.g., weather effects, differing crops or crop varieties). The zone assignments and distributions are estimated using stochastic expectation maximization (SEM) and the maximizer of the posterior marginals (MPM). The underlying assumption of the model and algorithm is that the yields corresponding to a given YPZ will behave similarly and therefore derive from the same probability distribution. YPZs are useful inputs for determining management zones. An advantage of this method is that it is able to run with only the yield data which are automatically collected during harvest. Also, this method requires no crop specific calibration or configuration or normalization of the data by year.

关键词： Hidden Markov models Image segmentation expectation-maximization algorithms Monte Carlo methods Yield Productivity zone Management zone

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Some applications of M-ary detection in quantitative finance

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QUANTITATIVE FINANCE 2010年第1期10卷 13-20页

作者： Malcolm, W. P. Elliott, R. J. Australian Natl Univ Inst Math Sci Canberra ACT 0200 Australia Univ Calgary Haskayne Sch Business Calgary AB T2N 1N4 Canada

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关键词： FINANCE -- Mathematical models CONVERGENCE (Economics) algorithms ECONOMICS expectation-maximization algorithms

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Adaptive Classification on Brain-Computer Interfaces Using Reinforcement Signals

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NEURAL COMPUTATION 2012年第11期24卷 2900-2923页

作者： Llera, A. Gomez, V. Kappen, H. J. Radboud Univ Nijmegen Nijmegen Netherlands Donders Inst Brain Cognit & Behav NL-6525 EZ Nijmegen Gelderland Netherlands

We introduce a probabilistic model that combines a classifier with an extra reinforcement signal (RS) encoding the probability of an erroneous feedback being delivered by the classifier. This representation computes the class probabilities given the task related features and the reinforcement signal. Using expectation maximization (EM) to estimate the parameter values under such a model shows that some existing adaptive classifiers are particular cases of such an EM algorithm. Further, we present a new algorithm for adaptive classification, which we call constrained means adaptive classifier, and show using EEG data and simulated RS that this classifier is able to significantly outperform state-of-the-art adaptive classifiers.

关键词： ADAPTIVE computing systems CLASSIFICATION BRAIN-computer interfaces FEEDBACK control systems expectation-maximization algorithms SIMULATION methods & models

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The spike-and-slab lasso Cox model for survival prediction and associated genes detection

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BIOINFORMATICS 2017年第18期33卷 2799-2807页

作者： Tang, Zaixiang Shen, Yueping Zhang, Xinyan Yi, Nengjun Soochow Univ Sch Publ Hlth Dept Biostat Suzhou 215123 Peoples R China Soochow Univ Coll Med Jiangsu Key Lab Prevent & Translat Med Geriatr Di Suzhou 215123 Peoples R China Soochow Univ Coll Med Ctr Genet Epidemiol & Genom Suzhou 215123 Peoples R China Univ Alabama Birmingham Dept Biostat Birmingham AL 35294 USA

Motivation: Large-scale molecular profiling data have offered extraordinary opportunities to improve survival prediction of cancers and other diseases and to detect disease associated genes. However, there are considerable challenges in analyzing large-scale molecular data. Results: We propose new Bayesian hierarchical Cox proportional hazards models, called the spike-and-slab lasso Cox, for predicting survival outcomes and detecting associated genes. We also develop an efficient algorithm to fit the proposed models by incorporating expectation-maximization steps into the extremely fast cyclic coordinate descent algorithm. The performance of the proposed method is assessed via extensive simulations and compared with the lasso Cox regression. We demonstrate the proposed procedure on two cancer datasets with censored survival outcomes and thousands of molecular features. Our analyses suggest that the proposed procedure can generate powerful prognostic models for predicting cancer survival and can detect associated genes. Availability and implementation: The methods have been implemented in a freely available R package BhGLM (http://***/bhglm/). Contact:nyi@*** Supplementary information: Supplementary data are available at Bioinformatics online.

关键词： CANCER HAZARDS expectation-maximization algorithms REGRESSION (Psychology) DRUGS

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